Intermediate Algebra (12th Edition)

by
Lial, Margaret L.; Hornsby, John; McGinnis, Terry

Answer

$|k^{5}|$

Work Step by Step

We know that $\sqrt[4] k^{20}=|k^{5}|$, because $(k^{5})^{4}=k^{5\times4}=k^{20}$.
Since $k$ is being raised to an odd positive power, we must use an absolute value sign to guarantee that the result is not negative (because $k^{5}$ is negative when $k$ is negative, and we know that there is no real number solution to $\sqrt[n] a$ when $a$ is negative and $n$ is even).